System, Method and Computer-Program Product for In-Situ Calibration of a Wellbore Resistivity Logging Tool

ABSTRACT

In-situ calibration of a resistivity logging tool is accomplished using a variety of methods in which deep measurement signals are calibrated using acquired and simulated measurement signals.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to calibration techniques forwellbore logging tools and, more specifically, to an in-situ calibrationmethod for a resistivity logging tool.

BACKGROUND

Among all logging tools deployed in the wellbore, resistivity toolsprovide the largest depth of detection. As a result, they have beenextensively used for detecting formation layer boundaries inapplications such as landing or well placement. Moreover, such loggingtools are utilized to acquire various other characteristics of earthformations traversed by the wellbore and data relating to the size andconfiguration of the wellbore itself. The collection of informationrelating to downhole conditions, commonly referred to as “logging,” canbe performed by several methods including wireline logging, “loggingwhile drilling” (“LWD”) and “measuring while drilling (“MWD”).

The depth of detection provided by the logging tool is directlyproportional to the distance between the transmitter and the receiver.As a result, most of the deep reading tools have very large distancebetween them. For example, some deep resistivity reading tools can be aslong as 50-100 feet, and they operate at frequencies lower than 8 KHz tocompensate for the geometrically increasing attenuation at largertransmitter receiver separations. In contrast, the standard, shallower,tools have a range of about 20 feet and they are optimized for placementof wells in reservoirs within about 10 feet from the top or bottomboundary of the reservoir rock.

The required distances between the transmitters and receivers along deepreading tools create problems in calibration since most of theconventional calibration methods (air hang, test tank, or oven, forexample) require a certain stand-off from any nearby objects that mightinterfere with the calibration measurement signals. As a result, it isimpractical to apply these conventional calibration techniques to a deepreading resistivity tool since the tool's sensitive volume is too largeand, thus, it is not feasible to have facilities big enough to fullycontain the tools.

Accordingly, there is a need in the art for a practical technique inwhich to calibrate a deep reading resistivity logging tool.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates an LWD logging tool that performs in-situcalibration of formation measurement signals taken along a hydrocarbonformation, according certain illustrative embodiments of the presentdisclosure;

FIG. 1B illustrates a wireline logging tool that performs in-situcalibration of formation measurement signals taken along a hydrocarbonformation, according certain illustrative embodiments of the presentdisclosure;

FIG. 2 is a block diagram of circuitry embodied within a logging toolnecessary to acquire the formation measurement signals, according tocertain illustrative embodiments of the present disclosure;

FIG. 3A is a flow chart detailing an in-situ calibration methodaccording to certain illustrative methodologies of the presentdisclosure;

FIGS. 3B-3D illustrates a illustrative logging tool of the presentdisclosure deployed in one or more calibration and/or application zonesalong a wellbore;

FIG. 4 is a flow chart detailing an in-situ calibration method wherebyan acquired deep measurement signal is calibrated using a modeled deepmeasurement signal, according to certain illustrative methodologies ofthe present disclosure;

FIG. 5A is a graph illustrating a modeled log response generated fromlook up tables, according to certain illustrative methodologies of thepresent disclosure;

FIGS. 5B-5G are graphs illustrating the calibration accuracy of themethod of FIG. 4 whereby calibration is performed at each depth;

FIG. 6A is a flow chart detailing an in-situ method whereby an acquireddeep measurement signal is calibrated using a modeled low frequencymeasurement signal, according to certain illustrative methodologies ofthe present disclosure;

FIG. 6B illustrates an illustrative logging tool deployed in acalibration zone, according to an alternate embodiment of the presentdisclosure; and

FIG. 7 is a graph illustrating the accuracy of the method of FIG. 6Ausing three different reference low frequencies measurement signals.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Illustrative embodiments and related methodologies of the presentdisclosure are described below as they might be employed in an in-situcalibration methodology for use with wellbore resistivity logging tools.In the interest of clarity, not all features of an actual implementationor methodology are described in this specification. It will of course beappreciated that in the development of any such actual embodiment,numerous implementation-specific decisions must be made to achieve thedevelopers' specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the art having the benefit ofthis disclosure. Further aspects and advantages of the variousembodiments and related methodologies of the disclosure will becomeapparent from consideration of the following description and drawings.

FIG. 1A illustrates a resistivity logging tool, utilized in an LWDapplication, that performs in-situ calibration of measurement signalstaken along a hydrocarbon formation, according certain illustrativeembodiments. The methodologies described herein may be performed by asystem control center located on the logging tool or may be conducted bya processing unit at a remote location, such as, for example, thesurface. Nevertheless, illustrative embodiments of the in-situcalibration methodology are based on two formation measurement signals,one being a calibrated measurement signal and the other being anuncalibrated measurement signal. In a first illustrative methodology, bytranslating a shallow reference measurement signal into a deepmeasurement signal, the present inventive methodologies normalize thedeep measurement signal with itself at selected calibration depths alongthe wellbore. In a second illustrative methodology, a deep low frequencymeasurement signal is utilized to calibrate the deep measurement signal.Thereafter, in either methodology, the calibrated deep measurementsignal is inverted to generate desired petrophysical characteristics ofthe borehole and surrounding geological formation (i.e., formationparameters) related to electrical or geological properties of theformation such as, for example, layer resistivities, distances ordirection to layer boundaries, 2D shape of arbitrary layer boundaries,or 3D distribution of formation resistivities. Accordingly, wellboreoperations may be conducted based upon the formation parameters such as,for example, drilling, well placement, landing or geosteeringoperations.

FIG. 1A illustrates a drilling platform 2 equipped with a derrick 4 thatsupports a hoist 6 for raising and lowering a drill string 8. Hoist 6suspends a top drive 10 suitable for rotating drill string 8 andlowering it through well head 12. Connected to the lower end of drillstring 8 is a drill bit 14. As drill bit 14 rotates, it creates awellbore 16 that passes through various layers of a formation 18. A pump20 circulates drilling fluid through a supply pipe 22 to top drive 10,down through the interior of drill string 8, through orifices in drillbit 14, back to the surface via the annulus around drill string 8, andinto a retention pit 24. The drilling fluid transports cuttings from theborehole into pit 24 and aids in maintaining the integrity of wellbore16. Various materials can be used for drilling fluid, including, but notlimited to, a salt-water based conductive mud.

A logging tool 26 is integrated into the bottom-hole assembly near thebit 14. In this illustrative embodiment, logging tool 26 is an LWD tool;however, in other illustrative embodiments, logging tool 26 may beutilized in a wireline or tubing-conveyed logging application. Loggingtool 26 may be, for example, an ultra-deep reading resistivity tool.Alternatively, non-ultra-deep resistivity logging tools may also beutilized in the same drill string along with the deep reading loggingtool. Persons ordinarily skilled in the art having the benefit of thisdisclosure will realize there are a variety of resistivity logging toolswhich may be utilized within the present disclosure. Moreover, incertain illustrative embodiments, logging tool 26 may be adapted toperform logging operations in both open and cased hole environments.Furthermore, in certain embodiments, the measurement signals utilized inthe calibration process may have originated from different boreholes,preferably in the same region of earth where a strong relationshipexists between the boreholes.

Still referring to FIG. 1A, as drill bit 14 extends wellbore 16 throughformations 18, logging tool 26 collects measurement signals relating tovarious formation properties, as well as the tool orientation andvarious other drilling conditions. In certain embodiments, logging tool26 may take the form of a drill collar, i.e., a thick-walled tubularthat provides weight and rigidity to aid the drilling process. However,as described herein, logging tool 26 includes an induction orpropagation resistivity tool to sense geology and resistivity offormations. A telemetry sub 28 may be included to transfer images andmeasurement data/signals to a surface receiver 30 and to receivecommands from the surface. In some embodiments, telemetry sub 28 doesnot communicate with the surface, but rather stores logging data forlater retrieval at the surface when the logging assembly is recovered.

Still referring to FIG. 1A, logging tool 26 includes a system controlcenter (“SCC”), along with necessary processing/storage/communicationcircuitry, that is communicably coupled to one or more sensors (notshown) utilized to acquire formation measurement signals reflectingformation parameters. In certain embodiments, once the measurementsignals are acquired, the system control center calibrates themeasurement signals and communicates the data back uphole and/or toother assembly components via telemetry sub 28. In an alternateembodiment, the system control center may be located at a remotelocation away from logging tool 26, such as the surface or in adifferent borehole, and performs the processing accordingly. These andother variations within the present disclosure will be readily apparentto those ordinarily skilled in the art having the benefit of thisdisclosure.

The logging sensors utilized along logging tool 26 are resistivitysensors, such as, for example, magnetic or electric sensors, and maycommunicate in real-time. Illustrative magnetic sensors may include coilwindings and solenoid windings that utilize induction phenomenon tosense conductivity of the earth formations. Illustrative electricsensors may include electrodes, linear wire antennas or toroidalantennas that utilize Ohm's law to perform the measurement. In addition,the sensors may be realizations of dipoles with an azimuthal momentdirection and directionality, such as tilted coil antennas. In addition,the logging sensors may be adapted to perform logging operations in theup-hole or downhole directions. Telemetry sub 28 communicates with aremote location (surface, for example) using, for example, acoustic,pressure pulse, or electromagnetic methodologies, as will be understoodby those ordinarily skilled in the art having the benefit of thisdisclosure.

As described above, logging tool 26 is, in this example, a deep sensinginduction or propagation resistivity tool. As will be understood bythose ordinarily skilled in the art having the benefit of thisdisclosure, such tools typically include one or more transmitter andreceiver coils that are axially separated along the wellbore 16. Thetransmitter coils generate alternating displacement currents in theformation 18 that are a function of conductivity. The alternatingcurrents generate voltage at the one or more receiver coils. In additionto the path through the formation 18, a direct path from the transmittercoil(s) to receiver coil(s) also exists. In induction tools, signal fromsuch path can be eliminated by the use of an oppositely wound andaxially offset “bucking” coil. In propagation tools, phase and amplitudeof the complex-valued voltage can be measured at certain operatingfrequencies. In such tools, it is also possible to measure phasedifference and amplitude rat between of the complex-valued voltages attwo axially spaced receivers. Furthermore, pulse-excitation excitationand time-domain measurement signals can be used in the place offrequency domain measurement signals. Such measurement signals can betransformed into frequency measurements by utilizing a Fouriertransform. The calibration methods described below are applicable to allof these signals and no limitation is intended with the presentedexamples. Generally speaking, a greater depth of investigation can beachieved using a larger transmitter-receiver pair spacing, but thevertical resolution of the measurement signals may suffer. Accordingly,logging tool 26 may employ multiple sets of transmitters or receivers atdifferent positions along the wellbore 16 to enable multiple depths ofinvestigation without unduly sacrificing vertical resolution.

FIG. 1B illustrates an alternative embodiment of the present disclosurewhereby a wireline logging tool performs in-situ calibration offormation measurement signals. At various times during the drillingprocess, drill string 8 may be removed from the borehole as shown inFIG. 1B. Once drill string 8 has been removed, logging operations can beconducted using a wireline logging sonde 34, i.e., a probe suspended bya cable 41 having conductors for transporting power to the sonde andtelemetry from the sonde to the surface. A wireline logging sonde 34 mayhave pads and/or centralizing springs to maintain the tool near the axisof the borehole as the tool is pulled uphole. Logging sonde 34 caninclude a variety of sensors including a multi-array laterolog tool formeasuring formation resistivity. A logging facility 43 collectsmeasurements from the logging sonde 34, and includes a computer system45 for processing and storing the measurements gathered by the sensors.

FIG. 2 shows a block diagram of circuitry 200 embodied within loggingtool 26 (or other logging tools described herein such as, for example,sonde 34) necessary to acquire the formation measurement signals,according to certain illustrative embodiments of the present disclosure.Logging tool 26 is comprised of one or more transmitters T1 . . . TN andreceivers R1 . . . RN, and associated antennas, placed within groovesalong logging tool 26, which may comprise, for example, magnetic dipolerealizations such as coiled, tilted coil, solenoid, etc. During loggingoperations, pulsed or steady-state signals are generated at thetransmitting antennas which interact with the formation and layerboundaries in the vicinity of logging tool 26 to produce electricalsignals (i.e., measurement signals) that are picked up by the receivers.Utilizing data acquisition unit 27, system control center 25 thencollects and calibrates the formation measurement signal using themethodologies described herein. Thereafter, system control center 25records the measurement signal data to buffer 29, applies datapre-processing (using data processing unit 30) for reducing thebandwidth requirement, and then communicates the data to a remotelocation (surface, for example) using communication units 32 (telemetrysub 28, for example). As previously described, however, the uncalibratedformation measurement signals may be transmitted to a remote locationwhere the calibration then conducted. Calibration of the formationmeasurement signals may be conducted remotely. However, in thoseembodiments in which the calibration is conducted by logging tool 26,tool response times may be improved and telemetry bandwidth to othertools along the downhole string may be increased.

Although not shown in FIG. 2, circuitry 200 includes at least oneprocessor embodied within system control center 25 and a non-transitoryand computer-readable storage, all interconnected via a system bus.Software instructions executable by the processor for implementing theillustrative calibration methodologies described herein in may be storedin local storage or some other computer-readable medium. It will also berecognized that the calibration software instructions may also be loadedinto the storage from a CD-ROM or other appropriate storage media viawired or wireless methods.

Moreover, those ordinarily skilled in the art will appreciate thatvarious aspects of the disclosure may be practiced with a variety ofcomputer-system configurations, including hand-held devices,multiprocessor systems, microprocessor-based or programmable-consumerelectronics, minicomputers, mainframe computers, and the like. Anynumber of computer-systems and computer networks are acceptable for usewith the present disclosure. The disclosure may be practiced indistributed-computing environments where tasks are performed byremote-processing devices that are linked through a communicationsnetwork. In a distributed-computing environment, program modules may belocated in both local and remote computer-storage media including memorystorage devices. The present disclosure may therefore, be implemented inconnection with various hardware, software or a combination thereof in acomputer system or other processing system.

System control center 25 may further be equipped with earth modelingcapability in order to provide and/or transmit subsurface stratigraphicvisualizations including, for example, geo science interpretation,petroleum system modeling, geochemical analysis, stratigraphic gridding,facies, net cell volume, and petrophysical property modeling. Inaddition, such earth modeling capability may model well traces,perforation intervals, as well as cross-sectional through the facies andporosity data. Illustrative earth modeling platforms include, forexample, DecisionSpace®, as well as its PerfWizard® functionality, whichis commercially available through Landmark Graphics Corporation ofHouston, Tex. However, those ordinarily skilled in the art having thebenefit of this disclosure realize a variety of other earth modelingplatforms may also be utilized with the present disclosure.

FIG. 3A is a flow chart detailing an in-situ calibration method 300according to certain illustrative methodologies of the presentdisclosure. To assist in illustrating method 300, FIGS. 3B-3D areprovided which show simplified illustrations of logging tool 26 (LWDtool, for example) deployed along wellbore 16. As described in moredetail below, FIG. 3B shows logging tool 26 deployed along a calibrationzone 40, FIG. 3C shows logging tool 26 deployed in an application zone42, and FIG. 3D shows logging tool 26 deployed in a subsequent zone 44.In this example, logging tool 26 comprises three antennas, namely atransmitter T, shallow receiver SR₁ to receive shallow measurementsignals, and a deep receiver DR₂ to receive deep measurement signals.However, more antennas may be utilized in alternative embodiments.Before logging tool 26 is deployed downhole, SR₁ is calibrated so thataccurate shallow reference measurement signals 31 may be obtaineddownhole to aid in the calibration of subsequently obtained deepmeasurement signals 33. Although one of each measurement signal 31,33 isillustrated, multiple signals may be acquired.

In certain other illustrative embodiments, although calibration zone 40is shown above application zone 42 and subsequent zone 44, it will beunderstood that logging tool 26 can be deployed by raising or loweringit along wellbore 16. Thus, as described herein, calibration zone 40 mayin fact be located below or horizontally adjacent to application zone 42or subsequent zones 44, etc.

Since the shallow reference measurement signals obtained by SR₁ arecalibrated, each is an accurate and trusted signal, assuming boreholeand invasion effects are addressed. Thus, as described herein, a“reference measurement signal” refers to a real and accurate measurementsignal obtained by logging tool 26, which may be shallow and calibrated.Such pre-deployment calibration of logging tool 26 may be achieved in avariety of ways, such as, for example, using bench calibration with aloop antenna, temperature characterization from test heating, or byutilizing a calibrated resistivity measurement signal using a rat ofmeasurement signals taken different transmitters and/or receivers alonglogging tool 26 (such as used in Halliburton's INSITE ADR™ resistivitytool or the LOGIQ ACRt™ System).

With reference to FIGS. 3A-3D, when it is desired to perform a loggingoperation, logging tool 26 is then deployed downhole to a firstcalibration zone 40 along formation 18 at block 302. First calibrationzone 40 comprises a series of wellbore depths D₁, D₂, D_(N). At block304, system control center 25, using various components (sensors,receivers, etc.) of logging tool 26, acquires one or more firstmeasurement signal(s) of formation 18 along depths first calibrationzone 40. As will be described in greater detail below, in certainmethodologies, the first measurement signal is a deep measurement signal33 which is utilized (along with calibrated reference measurement signal31) to calibrate another deep measurement signal 33. In otherillustrative embodiments, the first measurement signal is a deep lowfrequency measurement signal utilized to calibrate another deepmeasurement signal 33.

At block 306, system control center 25 simulates (or models) one or moresecond measurement signal(s) using the parameters of formation 18 alongfirst calibration zone 40. Such parameters may include, for example,layer resistivities, layer positions, layer boundary shapes, 3Dresistivity distribution, dip angle, strike angle, borehole radius,borehole resistivity, eccentricity or eccentricity azimuth. In certainembodiments, the second measurement signal is obtained from a simulatedresponse of the same transmitter-receiver pair utilized to obtain thefirst measurement signal.

At block 308, system control center 25 calculates one or morecalibration coefficients based on a comparison between the acquiredfirst measurement signal and the simulated second measurement signal. Toachieve this, system control center 25 utilizes one of the illustrativecalibration models described below to calculate the calibrationcoefficients along first calibration zone 40. As further describedbelow, the calibration coefficients may be used along first calibrationzone 40 or subsequent zones to calibrate various acquired measurementsignals.

At block 310, utilizing logging tool 26, system control center 25 thenacquires one or more third measurement signals of formation 18 alongfirst calibration zone 40 using the same transmitter/receiver pairutilized to obtain the first measurement signal(s) and the simulatedsecond measurement signal(s). Alternatively, however, the thirdmeasurement signals may be acquired along application zone 42 orsubsequent zones 44 along wellbore 16 or in a different wellborealtogether. Nevertheless, at block 312, system control center 25 thencalibrates the acquired third measurement signals using the calibrationcoefficients calculated at block 308. The calibrated acquired thirdmeasurement signals are then inverted to produce desired formationparameters which are mainly related to electrical or geologicalproperties of formation 18, such as layer resistivities, distances,direction to layers. Illustrative inversion techniques employed mayinclude, for example, pattern matching or iterative methods utilizinglook-up tables or numerical optimization based on forward modeling, aswill be understood by those ordinarily skilled in the art having thebenefit of this disclosure. Illustrative formation parameters mayinclude, for example, layer resistivities, layer positions, layerboundary shapes, 3D resistivity distribution, dip angle, strike angle,borehole radius, borehole resistivity, eccentricity or eccentricityazimuth.

At block 314, system control center 25 then outputs the calibratedacquired third measurement signal(s). Here, the output may take avariety of forms such as, for example, simply transmitting the data to aremote location (surface, for example) or outputting the data in areport or geological model. Accordingly, the acquired third measurementsignals are calibrated in-situ (while logging tool 26 is in wellbore 16,for example).

Thereafter, a variety of wellbore operations may be performed based uponthe formation parameters. For example, drilling decisions such aslanding, geosteering, well placement or geostopping decisions may beperformed. In the case of landing, as the bottom hole assembly drillingthe well approaches the reservoir from above, the reservoir boundariesare detected ahead of time, thus providing the ability to steer thewellbore into the reservoir without overshoot. In the case of wellplacement, the wellbore may be kept inside the reservoir at the optimumposition, preferably closer to the top of the reservoir to maximizeproduction. In the case of geostopping, drilling may be stopped beforepenetrating a possibly dangerous zone.

Moreover, in certain illustrative methodologies, the calibrationcoefficients are calculated at a low angle section of the wellbore(inclination<45 degrees, for example), and calibration is then appliedto third measurement signals acquired from a high angle section of thewellbore (inclination>45 degrees, for example).

The foregoing method 300 embodies a general overview of the illustrativemethodologies of the present disclosure. Below, more detailedalternative methodologies of the present disclosure will be described.As described therein, the acquired and simulated measurement signals maytake on a variety of forms. For example, the reference or simulatedmeasurement signals may be acquired from another wellbore which may ormay not have similar formation properties or be located within the samereservoir. However, having such commonalities may improve the accuracyof the calibration since the calibration would be performed in similarconditions. In other examples, the acquired first measurement signals,simulated second measurement signals, and the acquired third measurementsignals may all be deep measurement signals. Such deep measurementsignals may, for example, have a radial range of 25 feet or more, whilethe shallow signals have a range less than that (10 feet or less, forexample).

In yet another alternative methodology, the simulated second measurementsignal may be substantially depth invariant (i.e., the change of thesignal with respect to depth is small enough such that it is consideredconstant for all practical purposes). In certain embodiments, theshallow reference measurement signals may be obtained from a separatetransmitter and/or receiver along logging tool 26, as compared to thetransmitter-receiver pair utilized to acquire the deep measurementsignals. Alternatively, the shallow reference measurement signals may beobtained from an existing resistivity tool integrated into the bottomhole assembly of which logging tool 26 forms a part. These and otheralterations of the present disclosure will be understood to thoseordinarily skilled in the art having the benefit of this disclosure.

FIG. 4 is a flow chart detailing an in-situ calibration method 400whereby an acquired deep measurement signal (i.e., third measurementsignal) is calibrated using a modeled deep measurement signal (i.e.,second measurement signal) and a reference measurement signal, accordingto one or more alternative illustrative methodologies of the presentdisclosure. With reference to FIGS. 3B-4, as previously described,logging tool 26 is first deployed downhole into wellbore 16 to firstcalibration zone 40 at block 402. At block 404, system control center 25acquires one or more calibrated reference measurement signal(s) 31 alongthe depth of first calibration zone 40.

At block 406, system control center 25 calculates a layer resistivityprofile of the formation along first calibration zone 40 using theacquired reference measurement signals 31, which may be shallow,compensated, or both shallow and compensated. As understood by thoseordinarily skilled in the art, “compensated” refers to a weightedaverage of two or more measurement signals in the logarithmic amplitudeor phase domain. The calibrated reference measurement signals 31 are notnecessarily taken from the same transmitter-receiver pair utilized toobtain the deep measurement signals 33. In certain embodiments, theresistivity profile is calculated from interpretation of the referencemeasurement signal by use of inversion, which can be applied by variousmethodologies (a look up table that converts amplitude ratios or phasedifferences to resistivities, a tool coefficient that converts voltagesto conductivities, or using a numerical optimization algorithm that cansolve for layer resistivities given reference measurement signals, forexample). Such inversion methods are readily understood by thoseordinarily skilled in the art having the benefit of this disclosure.

At block 408, system control center 25 selects a set of calibrationdepths CD₁, CD₂, CD_(N) along first calibration zone 40. Calibrationdepth selection is important to optimize the accuracy of calibration forthe deep measurement signals (i.e., third measurement signals). Thedepths may be selected, for example, in the upper sections of the well,preferably where there are relatively small variations in theresistivity profile. In this example, relatively small may be defined asthe variation being smaller than at least 90% of all measurement depthsavailable. In other environments, threshold numbers can be usedgenerally between 70% and 95%. The particular number is chosen tooptimize calibration performance and it is a function of formationvariability and measurement noise. An alternative threshold may be basedon an absolute rate of change value, which may be selected and optimizedheuristically based on past experience with different wells, or wellsections.

In other words, the calibration coefficients may be calculated at depthsthat satisfy a criterion based on a rate of change in the acquired deepmeasurement signals as a function of depth. In certain illustrativeembodiments, the criterion comprises selection of depths that have arate of change below a threshold value that is small enough to minimizethe calibration error, but large enough to provide a sufficient numbercalibration points necessary to perform the calculations. As an example,threshold can be chosen to be 90% point of the histogram of rate ofchange with respect to depth (i.e., the rate of change at which 90% ofall rate of change values are larger and 10% of all rate of changevalues are smaller). Other threshold numbers, typically between 75% and95%, could also be used. The particular number is chosen to optimizecalibration performance and it is a function of formation variabilityand measurement noise. An alternative threshold may be based on anabsolute rate of change value. This value can be selected and optimizedheuristically based on past experience with different wells, or wellsections. In addition, the amount of invasion in the referencemeasurement signal is also critical, as depths are preferably chosen informations where no invasion is expected. An illustrative optimumcalibration depth selection methodology will be provided in an examplebelow.

At block 410, utilizing logging tool 26, system control center 25acquires one or more deep measurement signals 33 (i.e., firstmeasurement signals) along first calibration zone 40 of formation 18. Incertain embodiments, the selected depths at which to acquire the deepmeasurement signals 33 may be different compared to the selectedcalibration depths CD₁, CD₂, CD_(N). In such embodiments, aninterpolation or extrapolation operation on deep measurement signals 33can be conducted to estimate the corresponding signals at depths CD₁,CD₂, CD_(N), which are then used in the subsequent steps.

At block 412, system control center 25 models one or more deepmeasurement signals (i.e., second measurement signals) using theresistivity profile of the formation layers at the selected calibrationdepths CD₁, CD₂, CD_(N) using the same transmitter-receiver pair (T-DR₂)utilized to obtain the deep measurement signals 33 (i.e., firstmeasurement signals) at block 410. In one illustrative methodology, thismodeling can be achieved by solution of Maxwell's equations or adifferent equation derived from Maxwell's equations that can solve forthe signals at the receivers given the transmitted signal and theformation electrical parameters (the most important of which isformation resistivity). For the formation, simplified models may be usedoccasionally to improve speed of computation. These models may include,for example, zero-dimensional (0D) models where the formationresistivity profile is constant in all three dimensions, one-dimensional(1D) models where the formation resistivity profile is constant in twodimensions, two-dimensional (2D) models where the formation resistivityprofile is constant in one dimension, and three-dimensional (3D) modelswhere the formation resistivity profile is varying in all threedimensions. In addition, solution of Maxwell's equations may be obtainedthrough analytical or semi-analytical expressions, finite-difference,finite-element, integral equation or methods of moments algorithms, aswill be understood by those ordinarily skilled in the art having thebenefit of this disclosure. The following analytical function may beutilized to represent this:

V _(cm)(z _(i))=MODEL(R(z))  Eq. (1), where

V_(cm) is the compensated simulated (deep) measurement, z_(i) is theaxial direction with respect to wellbore 16, R is the resistivity of theformation layers, and MODEL is the Electromagnetic Model described abovein relation to block 412. Using this illustrative embodiment, allpossible effects of the deep measurement signal(s) acquired at block 410should be taken into effect during modeling such as, for example, theeffects of the tool body presence, borehole fluid, antenna enclosures,frequency dispersive characteristic of resistivity, etc. Such effectsare important because any mismatch between the simulated/modeled andreal (acquired) measurement signals will result in inaccuratecalibration coefficients and/or inaccurate calibration.

At block 414, system control center 25 thenselects/interpolates/extrapolates deep measurement signal(s) 33 acquiredat block 410 at the selected calibration depths CD₁, CD₂, CD_(N). Atblock 416, system control center 25 then calculates the calibrationcoefficients using deep measurement signal(s) 33 (i.e., firstmeasurement signals) acquired at block 410 and the simulated deepmeasurement signal(s) (i.e., second measurement signals).

To achieve this, system control center 25 performs a comparison of deepmeasurement signal(s) 33 (i.e., first measurement signals) acquired atblock 410 and the simulated deep measurement signal(s) (i.e., secondmeasurement signals) to determine the calibration coefficients using thefollowing equations:

V _(cm)(z _(i))=F(V _(d)(z _(i)))  Eq. (2).

For example, V_(cm)(z_(i))=A×V_(d)(z_(i))+B, where F is the calibrationmodel, V_(d) is deep measurement signal acquired at block 410, A is again and B is an offset which is one or more calibration coefficientsassociated with the calibration model. Calibration model F, may be apolynomial of another analytical function.

At block 418, logging tool 26 obtains additional deep measurementsignal(s) (i.e., third measurement signals). These deep measurementsignals (i.e., third measurement signals) may be acquired alongcalibration zone 40, or in subsequent zones along formation 18 andcalibrated using the calibration coefficients determined along firstcalibration zone 40. Such deep measurement signals may also berepresented by numeral 33, although they are not illustrated as such forsimplicity. At block 420, system control center 25 calibrates theacquired deep measurement signal(s) (i.e., third measurement signals)using the calibration coefficients via the following equation:

V _(dc)(z)=F(V _(d)(z))  Eq. (3),

where V_(dc)(z) is the calibrated acquired deep measurement signal(s)(i.e., third measurement signals). As previously mentioned, the deepmeasurement signals acquired at block 418 may be measured along firstcalibration zone 40 or a subsequent zone, and calibrated as previouslydescribed. In the latter approach, with reference to FIGS. 3C-3D,logging tool 26 may be moved (e.g., raised or lowered) to an applicationzone 42 located along a range of wellbore depths which differ from thedepths of first calibration zone 40. As logging tool 26 is moved alongapplication zone 42, one or more deep measurement signals (i.e., thirdmeasurement signals) are acquired and calibrated using the calibrationcoefficients calculated along first calibration zone 40. Nevertheless,in either embodiment, at block 422, system control center 25 thenoutputs the calibrated acquired deep measurement signal(s) as previouslydescribed. Moreover, logging tool 26 may then be deployed further tosubsequent zone 44 whereby further deep measurement signals are obtainedand calibrated using the calibration coefficients.

To further demonstrate an illustrative calibration method, an examplewill now be discussed with reference to FIGS. 5A and 5B. FIG. 5Aillustrates a modeled log response generated from 0D inversion using anillustrative methodology described herein. The log charts wellbore depthin feet versus formation resistivity. Details of an illustrative loggingtool 26 are also shown in the insert of FIG. 5A. Four uppermost antennasA1-A4 are used to acquire the compensated shallow reference measurementsignals above logging tool 26, where antennas A1-A4 are axially orientedcoil transmitters and A2 and A3 are tilted coiled receivers.

The deep antenna A5, which is the lowermost antenna, is placed as low aspossible in the bottom hole assembly, which is in practice next to thebit to maximize depth of detection. In this illustrative embodiment,antenna A5 is 568 inches below antenna A4, antenna A4 is positioned 12inches below antenna A3, antenna A3 is positioned 8 inches below antennaA2, and antenna A2 is positioned 12 inches below antenna A1.

In this example, the deep antenna A5 is a receiver that is used inconjunction with antenna A1 (transmitter), but at a different frequencywhen compared to the shallow signal. Two frequencies of operation wereused: 500 KHz for the calibrated shallow measurement signal (2 feetrange), which is excited from antennas A1/A4 and received by antennasA2/A3, respectively; and 5 KHz for the deep measurement signal (50 feetrange), which is excited from antenna A1 and received by antenna A5. Itis noted here that the four measurement signals that are received fromcombinations of A1,A4 transmitters and A2,A3 receivers are processed toproduce a single compensated signal, as understood in the art ofinduction well logging with tools such as Halliburton's INSITE ADR™ orLOGIQ ACRt™. In this example, no calibration error for the deepmeasurement signal is assumed, so the deep measurement signal that isshown is the ideal response which is not available in practice. Relativedip angle of the formations, θ_(dip), is assumed to be zero degrees inthis example without loss of generality of the method. It can be seenfrom the synthetic log that the calibrated shallow measurement signalsdefine the formation boundary positions, while the deep measurementsignal averages out multiple layers at once. The shallow measurementsignal in FIG. 5A will be input to the various methods described herein.The deep measurement signal is shown only as a reference. In thisexample, method 400, and a 1D formation model with a resistivity profilegiven by the shallow resistivity curve in FIG. 5A, is used.

FIGS. 5B-5G are graphs illustrating the calibration accuracy of method400 where calibration coefficients are computed from the shallow sectionand applied to the deep section repeatedly at each depth. FIGS. 5B-5Eshows the calibrated deep measurement signal as an output of the method400, as well as the ideal deep measurement signal taken from FIG. 5A. Asshown, the calibrated and ideal amplitude (5B), phase (5C), amplituderesistivity (5D), and phase resistivity (5E) are each plotted verses thedepth. The closeness of the two curves illustrates how well method 400is operating. In these examples, a multiplicative model is used forcorrection F(V_(d))=KV_(d), where K is a calibration coefficientcalculated and applied to data measured at the same depth. It can beseen from the last two subfigures that the error in calibration is about0.5% and 1 degree maximum. However, as previously mentioned, depthselection is important to optimize the accuracy of calibration for thedeep measurement signal, thus improving accuracy. It can be seen fromFIGS. 5F (plots % error in Amplitude) and 5G (plots error in phase) thataccuracy is maximized at minimum and maximum peaks of the log (i.e.,when the derivative of the resistivity, amplitude or phase curves areclose to zero).

Therefore, in some illustrative embodiments, calibration should beapplied only at depths CD₁, CD₂, CD_(N) which correspond to the peaks,or zero slopes ZS (FIGS. 5B-5E), of the resistivity curves of the logresponse. After each peak, the resulting calibration coefficients may beused in the subsequent depth points (i.e., subsequent zones), aspreviously described. Accordingly, through use of this alternativemethod, the accuracy of the calibration methods describes herein issignificantly improved.

In general, calibration performed at every depth is valid in thevicinity of that depth, since temperature characteristic does not varysignificantly. However, as logging tool 26 moves to substantiallydifferent temperatures, its characteristics usually drifts and, thus,calibration needs to be repeated. Since it is not straightforward todetect drifts in tool characteristics, calibration needs to beperiodically applied, for example, at calibration depths CD₁, CD₂,CD_(N) that correspond to every peak of the resistivity curves in agiven calibration zone, or in pre-determined periods. Therefore, certainillustrative embodiments of the present disclosure may also periodicallyre-calculate calibration coefficients (i.e., recalibrate) logging tool26 using any of the methodologies described herein. In such embodiments,for example, with reference to FIGS. 3B-3D, logging tool 26 may bedeployed to first calibration zone 40 where the calibration coefficientsare determined, and then deployed down to application zone 42 where thedeep measurement signals are acquired and calibrated using thecalibration coefficients. Simultaneously, logging tool 26 may repeat thefunctions necessary to calculate new calibration coefficients usingmeasurement signals acquired and modeled along application zone 42(which essentially makes application zone 42 a second calibration zone).The new calibration coefficients may then be utilized to calibrate deepmeasurement signals (i.e., fourth measurement signals) acquired in thesecond calibration zone or a subsequent third calibration zone 44. Alsonote there may be overlap in the calibration/application depths.Ultimately, however, this process may be repeated as desired. Since ashallow measurement signal is typically is not available in the vicinityof the effective deep measurement signal depth immediately after it isacquired, an extrapolation of calibration coefficients can be performedto estimate the calibration coefficients that correspond to theeffective depth of the deep measurement signal.

FIG. 6A illustrates a flow chart detailing an in-situ method 600 wherebyan acquired deep measurement signal (i.e., third measurement signals) iscalibrated using one or more simulated low frequency measurementsignal(s) (i.e., second measurement signal) and low frequencymeasurement signal(s) (i.e., first measurement signal). The lowfrequency measurement signal(s) have a frequency low enough such thatthe signal is not affected by variations along formation 18. In otherwords, the frequency should be low enough such that the received lowfrequency measurement signal is substantially independent of thepractical range of formation conductivity. Thus, no resistivity profileis necessary since the low frequency measurement signal is not sensitiveto it. This may be, for example, 500 Hz for a 50 feet logging tool, withthe frequency being proportional to the inverse of the distance-squared(˜K/(d²)), where K is a constant factor and d is the distance. Inanother example using a 100 feet tool, the frequency may be 125 Hz for asimilar error. The required frequencies may be determined and adjustedas necessary, as will be understood by those ordinarily skilled personsdescribed herein.

FIG. 6B illustrates an illustrative logging tool of the presentdisclosure deployed in a calibration zone along a drill string 8.However, in other illustrative embodiments, the logging tool may bedeployed via a wireline or other deployment methodology as previouslydescribed. Nevertheless, in FIG. 6B, logging tool 26 is similar to thosepreviously described except that, in FIG. 6B, logging tool 26 onlyincludes two antennas T and DR₂. With reference to FIG. 6B, at block602, just as previously described, logging tool 26 is deployed downholeto first calibration zone 40. At block 604, system control center 25simulates a deep low frequency measurement signal V_(im) (i.e., secondmeasurement signal) along first calibration zone 40 of formation 18using the same transmitter-receiver pair (T-DR₂) used to obtain the deepmeasurement signals. At block 606, system control center 25, usinglogging tool 26, acquires one or more deep low frequency measurementsignals 33, V_(i)(z) (i.e., first measurement signals). After the lowfrequency measurement signals 33 are applied to formation 18, thereceived signals are recorded by system control center 25. Since the lowfrequency measurement signals 33 are not affected by the formationproperties, they can be compared to a constant (pre-calculated, forexample) reference from modeling and a calibration function is thencalculated as described below. For example, the constant referencesignal may be generated by performing modeling with a fixed (andhigh>1000 Ohm, for example) formation resistivity. As described inpreviously methodologies, the calibration coefficients generated usingthe calibration function are applied to the deep measurement signals(i.e., third measurement signals) that have been acquired or that willbe acquired at subsequent depths.

At block 608, system control center 25 calculates the calibrationcoefficients using the simulated deep low frequency measurementsignal(s) (i.e., second measurement signals) and the acquired deep lowfrequency measurement signals 33 (i.e., first measurement signals).Here, system control center 24 makes a comparison between the simulatedlow frequency measurement signal(s) (i.e., second measurement signals)and the acquired low frequency measurement signal(s) 33 (i.e., firstmeasurement signals) to determine the calibration coefficients. Thefollowing equation may be utilized:

C(z)=F(V _(im) *V _(i)(z))  Eq. (4),

where, V_(im) is the modeled deep signal, and V_(i)(z) is the measureddeep signal 33, for example, C(z)=V_(im)/V_(i)(z). Although notillustrated, at block 610, as described in FIGS. 3B-3D, system controlcenter 25 acquires one or more deep measurement signal(s), V_(d)(z),(i.e., third measurement signals) along first calibration zone 40 orsubsequent zones. At block 612, system control center 25 calibrates theacquired deep measurement signal(s) (i.e., third measurement signals)using the calibration coefficients using, for example:

V _(dc)(z)=C(z)*V _(d)(z)  Eq. (5).

At block 614, system control center 25 then outputs the calibratedacquired deep measurement signal(s) (i.e., third measurement signals) aspreviously described. Accordingly, a deep low frequency measurementsignal may be utilized to calibrate an acquired deep measurement signalin-situ.

FIG. 7 is a graph showing the accuracy of method 600 using threedifferent low frequencies measurement signals. FIG. 7 plots the wellboredepth versus phase resistivity for frequency references at 100 Hz_(i)250 Hz_(i) 500 Hz and a theoretically ideal calibrated signal. Detailsof an illustrative logging tool 26 are also shown in the insert of FIG.7. Two antennas A1 and A2, spaced 600 inches apart, are used to acquirethe low frequency measurement signals. The deep antenna A2 is placed atthe bottom of logging tool 26, which is in practice next to the bit tomaximize depth of detection, at an angle of 45°. The relative dip angleof the formation, θ_(dip), in this example is assumed to be zero withoutloss of generality.

As can be seen, lower frequencies are better references, and the 100 Hzsignal reduces the error to a negligible value. Therefore, in thisexample, calibration that is conducted at this frequency should beaccurate enough to allow interpretation of the calibrated data. Itshould be noted here that low frequencies result in smaller signallevels since signals from the coils are proportional to the frequenciesfor a constant current supply. However, this can be negated by havingmore numbers of turns for the coils, which increases the sensor size. Inone illustrative embodiment of logging tool 26, it is possible to applythe low frequency measurement signal simultaneously with the deepmeasurement signal to make sure these two measurements are made at thesame electrical/mechanical conditions. This can reduce the errors in thecalibration. Finally, the frequency of the low frequency measurementsignal used as the reference can be adapted based on the expected ormeasured resistivity of the formations, which will optimize the signallevels as well as measurement accuracy.

Embodiments of the present disclosure described herein further relate toany one or more of the following paragraphs:

1. A method for in-situ calibration of a logging tool deployed along awellbore, the method comprising acquiring a first measurement signal ofa formation using the logging tool; simulating a second measurementsignal of the formation; calculating a calibration coefficient based ona comparison between the acquired first measurement signal and thesimulated second measurement signal; acquiring a third measurementsignal of the formation using the logging tool, wherein the first,second and third measurement signals correspond to the sametransmitter-receiver pair of the logging tool; and calibrating theacquired third measurement signal using the calibration coefficient.

2. A method as defined in paragraph 1, wherein the acquired firstmeasurement signal, simulated second measurement signal, and acquiredthird measurement signal are all deep measurement signals.

3. A method as defined in any of paragraphs 1-2, wherein simulating thesecond measurement signal further comprises acquiring a referencemeasurement signal of the formation using the logging tool; calculatinglayer resistivity data of the formation using the acquired referencemeasurement signal; selecting a set of calibration depths along thewellbore; and simulating the second measurement signal at the selectedcalibration depths using the layer resistivity data.

4. A method as defined in any of paragraphs 1-3, wherein the referencemeasurement signal is a shallow measurement signal.

5. A method as defined in any of paragraphs 1-4, wherein the firstmeasurement signal is acquired at a depth which corresponds to at leastone of the selected set of calibration depths.

6. A method as defined in any of paragraphs 1-5, wherein the referencemeasurement signal is acquired within a first calibration zone of theformation, the first calibration zone being a first range of wellboredepths; the first measurement signal is acquired within the firstcalibration zone; the second measurement signal is simulated within thefirst calibration zone; and the third measurement signal is acquiredwithin an application zone located along a second range of wellboredepths different from the first calibration zone.

7. A method as defined in any of paragraphs 1-6, wherein selecting theset of calibration depths further comprises generating a log response ofa plurality of acquired first measurement signals; and selecting thosecalibration depths which correspond to zero slopes along the logresponse.

8. A method as defined in any of paragraphs 1-7, wherein the acquiredfirst measurement signal is a low frequency signal comprising afrequency low enough such that the acquired first measurement signal isnot affected by variations in the formation.

9. A method as defined in any of paragraphs 1-8, wherein the acquiredfirst and third measurement signals are deep measurement signals.

10. A method as defined in any of paragraphs 1-9, wherein the simulatedsecond measurement signal is substantially depth invariant.

11. A method as defined in any of paragraphs 1-10, wherein the firstmeasurement signal is acquired within a first calibration zone of theformation, the first calibration zone being a first range of wellboredepths; the second measurement signal is simulated within the firstcalibration zone; and the third measurement signal is acquired within anapplication zone located along a second range of wellbore depthsdifferent from the first calibration zone.

12. A method as defined in any of paragraphs 1-11, further comprisingacquiring a fourth measurement signal within a second calibration zoneof the formation, the second calibration zone being a third range ofwellbore depths different from the first calibration zone; andcalibrating the acquired fourth measurement signal.

13. A method as defined in any of paragraphs 1-12, wherein calculatingthe calibration coefficient further comprises utilizing a calibrationmodel to calculate a plurality of calibration coefficients along acalibration zone of the formation, the calibration zone being a firstrange of wellbore depths, wherein the third measurement signal isacquired and calibrated within an application zone located along asecond range of wellbore depths different from the calibration zone.

14. A method as defined in any of paragraphs 1-13, wherein calculatingthe calibration coefficient further comprises utilizing a calibrationmodel to calculate a plurality of calibration coefficients along acalibration zone of the formation, the calibration zone being a firstrange of wellbore depths, wherein the third measurement signal isacquired and calibrated within the calibration zone.

15. A method as defined any of paragraphs 1-14, wherein the calibrationmodel is a polynomial function.

16. A method as defined in any of paragraphs 1-15, wherein thecalibration model is F(X)=AX, where A is a calibration coefficient.

17. A method as defined in any of paragraphs 1-16, wherein thecalibration model is F(X)=AX+B, where A and B are the calibrationcoefficients.

18. A method as defined in any of paragraphs 1-17, wherein thecalibration coefficients are calculated at depths that satisfy acriterion based on a rate of change in third measurement signal as afunction of depth.

19. A method as defined in any of paragraphs 1-18, wherein the criterioncomprises selection of depths that have a rate of change below athreshold value.

20. A method as defined in any of paragraphs 1-19, wherein the simulatedsecond measurement signal is simulated using parameters of the formationin which the logging tool is deployed; parameters of another formationin which the logging tool is not deployed; or a constant formationresistivity.

21. A method as defined in any of paragraphs 1-20, wherein the firstmeasurement signal corresponds to the transmitter-receiver pair of thesecond and third measurement signals.

22. A method as defined in any of paragraphs 1-21, wherein the loggingtool forms part of a logging while drilling or wireline assembly.

23. A method as defined in any of paragraphs 1-22, wherein calculatingthe calibration coefficient further comprises calculating thecalibration coefficient at a low angle section of the wellbore, whereinthe third measurement signal is acquired from a high angle section ofthe wellbore.

Moreover, the foregoing paragraphs and other methodologies describedherein may be embodied within a system comprising processing circuitryto implement any of the methods, or a in a computer-program productcomprising instructions which, when executed by at least one processor,causes the processor to perform any of the methods described herein.

Although various embodiments and methodologies have been shown anddescribed, the disclosure is not limited to such embodiments andmethodologies and will be understood to include all modifications andvariations as would be apparent to one skilled in the art. Therefore, itshould be understood that the disclosure is not intended to be limitedto the particular forms disclosed. Rather, the intention is to cover allmodifications, equivalents and alternatives falling within the spiritand scope of the disclosure as defined by the appended claims.

1. A method for in-situ calibration of a logging tool deployed along awellbore, the method comprising: acquiring a first measurement signal ofa formation using the logging tool; simulating a second measurementsignal of the formation; calculating a calibration coefficient based ona comparison between the acquired first measurement signal and thesimulated second measurement signal; acquiring a third measurementsignal of the formation using the logging tool, wherein the first,second and third measurement signals correspond to the sametransmitter-receiver pair of the logging tool; and calibrating theacquired third measurement signal using the calibration coefficient. 2.A method as defined in claim 1, wherein the acquired first measurementsignal, simulated second measurement signal, and acquired thirdmeasurement signal are all deep measurement signals.
 3. A method asdefined in claim 1, wherein simulating the second measurement signalfurther comprises: acquiring a reference measurement signal of theformation using the logging tool; calculating layer resistivity data ofthe formation using the acquired reference measurement signal; selectinga set of calibration depths along the wellbore; and simulating thesecond measurement signal at the selected calibration depths using thelayer resistivity data.
 4. A method as defined in claim 3, wherein thereference measurement signal is a shallow measurement signal.
 5. Amethod as defined in claim 3, wherein the first measurement signal isacquired at a depth which corresponds to at least one of the selectedset of calibration depths.
 6. A method as defined in claim 3, wherein:the reference measurement signal is acquired within a first calibrationzone of the formation, the first calibration zone being a first range ofwellbore depths; the first measurement signal is acquired within thefirst calibration zone; the second measurement signal is simulatedwithin the first calibration zone; and the third measurement signal isacquired within an application zone located along a second range ofwellbore depths different from the first calibration zone.
 7. A methodas defined in claim 3, wherein selecting the set of calibration depthsfurther comprises: generating a log response of a plurality of acquiredfirst measurement signals; and selecting those calibration depths whichcorrespond to zero slopes along the log response.
 8. A method as definedin claim 1, wherein the acquired first measurement signal is a lowfrequency signal comprising a frequency low enough such that theacquired first measurement signal is not affected by variations in theformation.
 9. A method as defined in claim 8, wherein the acquired firstand third measurement signals are deep measurement signals.
 10. A methodas defined in claim 8, wherein the simulated second measurement signalis substantially depth invariant.
 11. A method as defined in claim 8,wherein: the first measurement signal is acquired within a firstcalibration zone of the formation, the first calibration zone being afirst range of wellbore depths; the second measurement signal issimulated within the first calibration zone; and the third measurementsignal is acquired within an application zone located along a secondrange of wellbore depths different from the first calibration zone. 12.A method as defined in claim 6 or 11, further comprising: acquiring afourth measurement signal within a second calibration zone of theformation, the second calibration zone being a third range of wellboredepths different from the first calibration zone; and calibrating theacquired fourth measurement signal.
 13. A method as defined in claim 1,wherein calculating the calibration coefficient further comprisesutilizing a calibration model to calculate a plurality of calibrationcoefficients along a calibration zone of the formation, the calibrationzone being a first range of wellbore depths, wherein the thirdmeasurement signal is acquired and calibrated within an application zonelocated along a second range of wellbore depths different from thecalibration zone.
 14. A method as defined in claim 1, whereincalculating the calibration coefficient further comprises utilizing acalibration model to calculate a plurality of calibration coefficientsalong a calibration zone of the formation, the calibration zone being afirst range of wellbore depths, wherein the third measurement signal isacquired and calibrated within the calibration zone.
 15. A method asdefined claim 13 or 14, wherein the calibration model is a polynomialfunction.
 16. A method as defined in claim 15, wherein the calibrationmodel is F(X)=AX, where A is a calibration coefficient.
 17. A method asdefined in claim 15, wherein the calibration model is F(X)=AX+B, where Aand B are the calibration coefficients.
 18. A method as defined in claim13 or 14, wherein the calibration coefficients are calculated at depthsthat satisfy a criterion based on a rate of change in third measurementsignal as a function of depth.
 19. A method as defined in claim 18,wherein the criterion comprises selection of depths that have a rate ofchange below a threshold value.
 20. A method as defined in claim 1,wherein the simulated second measurement signal is simulated using:parameters of the formation in which the logging tool is deployed;parameters of another formation in which the logging tool is notdeployed; or a constant formation resistivity.
 21. A method as definedin claim 1, wherein the first measurement signal corresponds to thetransmitter-receiver pair of the second and third measurement signals.22. A method as defined in claim 1, wherein the logging tool forms partof a logging while drilling or wireline assembly.
 23. A method asdefined in claim 1, wherein calculating the calibration coefficientfurther comprises calculating the calibration coefficient at a low anglesection of the wellbore, wherein the third measurement signal isacquired from a high angle section of the wellbore.
 24. A systemcomprising processing circuitry to implement the methods of claim
 1. 25.A computer-program product comprising instructions which, when executedby at least one processor, causes the processor to perform any themethods of claims 1.